You have much more cold weather experience than I do. Coldest I have ever been in was 5F, and I was sleeping on foam. I do sleep in the 20's F and the past couple of years have been using a BA IAC.
It seems to me that if one is sleeping on a air mattress and the air inside of it is cold enough to freeze the water vapor from blowing it up, and there is still ice in it when you wake up, then one would lose a lot of body heat into the air mattress during the night? Of course if one had thick enough foam pads on top of the air mattress to stop the heat loss, then an air mattress would not be needed?
Not being argumentative or smart -- just trying to figure all of this out.
P.S. Sleeping in -24F weather does not seem like fun or sane :)